A brief introduction to spectral graph theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
European Mathematical Society
[2018]
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| Schriftenreihe: | EMS textbooks in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | viii, 156 Seiten Illustrationen 23.5 cm x 16.5 cm |
| ISBN: | 9783037191880 3037191880 |
Internformat
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| 653 | |a Cayley graphs | ||
| 653 | |a Laplacian eigenvalues of graphs | ||
| 653 | |a adjacency eigenvalues of graphs | ||
| 653 | |a algebraic graphs over finite fields | ||
| 653 | |a character sums | ||
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Datensatz im Suchindex
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| adam_text | Contents Introduction.................. ...................................................... .. ......................... . 1 1 Graphs.......................................................... 1.1 Notions........................ 1.2 Bipartite graphs.................................................................................. 3 3 7 2 Invariants................................................. .............................. .................. 2.1 Chromatic number and independencenumber .................................. 2.2 Diameter and girth............................................................ 2.3 Isoperimetric number........................... .. 11 11 12 15 3 Regular graphs......................................................................................... ... . 3.1 Cayley graphs..................................................................... 3.2 Cayley graphs, continued.............................. . . . ..... . . 3.3 Strongly regular graphs . ... . . . . . . 3.4 Design graphs . ...... .... ... . . . . ............... ... . . . . . 19 19 22 26 29 4 Finite fields................... .... ........................................... ... ... 31 4.1 Notions........................................................................... 31 4.2 Projective combinatorics........................... ................... . . · · 33 4.3 Incidence graphs................................................... 36 5 Squares in finite fields....................................................................................... 39 5.1 The quadratic
character............................................................ 39 5.2 Quadratic reciprocity....................................... 42 5.3 Paley graphs .................................................... .... . . ... . . . 44 5.4 A comparison............................................................... 47 6 Characters....................................................................................... 6.1 Characters of finite abelian groups.............................. 6.2 Character sums over finite fields....................................................... 6.3 More character sums over finite fields.......................................... . 6.4 An application to Paley graphs......................................................... 51 51 53 57 59
viii Contents 7 Eigenvalues of graphs............................................................................................63 7.1 Adjacency and Laplacian eigenvalues ................................................ 63 7.2 First properties..................................................................................... 65 7.3 First examples............................... 68 8 Eigenvalue computations.......................................................................................73 8.1 Cayley graphs and bi-Cayley graphs of abelian groups...................... 73 8.2 Strongly regular graphs......................................................................... 76 8.3 Two gems............................................................................................... 78 8.4 Design graphs............................... 80 9 Largest eigenvalues................................................................................................ 85 9.1 Extremal eigenvalues of symmetric matrices ....................................... 85 9.2 Largest adjacency eigenvalue . . . . . ................... 86 9.3 The average degree......................... 88 9.4 A spectral Ihran theorem............................................... 91 9.5 Largest Laplacian eigenvalue of bipartite graphs................................ 93 9.6 Subgraphs............................................................................................... 94 9.7 Largest eigenvalues of trees.................................................................. 97 10 More
eigenvalues.................................................. 103 10.1 Eigenvalues of symmetric matrices: Courant-Fischer.......................... 103 10.2 A bound for the Laplacian eigenvalues............................ 104 10.3 Eigenvalues of symmetric matrices: Cauchy and Weyl.......................... 107 10.4 Subgraphs...................................................................................................109 11 Spectral bounds.................................................................................................... 113 11.1 Chromatic number and independence number....................................... 113 11.2 Isoperimetric constant............................................ 116 11.3 Edge counting........................................................................................ 122 12 Farewell................................................................. 127 12.1 Graphs without 4-cycles ..........................................................................127 12.2 The Erdos-Rényi graph.............................................................................128 12.3 Eigenvalues of the Erdos-Rényi graph....................................................130 Further reading........................................................................................................... 135 Solutions to exercises..................................... 137 Index............................................................................................................................157
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| author | Nica, Bogdan 1977- |
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| bvnumber | BV045126096 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-10T08:09:26Z |
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| isbn | 9783037191880 3037191880 |
| language | English |
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| physical | viii, 156 Seiten Illustrationen 23.5 cm x 16.5 cm |
| publishDate | 2018 |
| publishDateSearch | 2018 |
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| publisher | European Mathematical Society |
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| series2 | EMS textbooks in mathematics |
| spelling | Nica, Bogdan 1977- Verfasser (DE-588)1156786754 aut A brief introduction to spectral graph theory Bogdan Nica Zürich European Mathematical Society [2018] © 2018 viii, 156 Seiten Illustrationen 23.5 cm x 16.5 cm txt rdacontent n rdamedia nc rdacarrier EMS textbooks in mathematics Kombinatorik (DE-588)4031824-2 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf undergraduate and graduate students Cayley graphs Laplacian eigenvalues of graphs adjacency eigenvalues of graphs algebraic graphs over finite fields character sums Kombinatorik (DE-588)4031824-2 s Graphentheorie (DE-588)4113782-6 s DE-604 European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030516192&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nica, Bogdan 1977- A brief introduction to spectral graph theory Kombinatorik (DE-588)4031824-2 gnd Graphentheorie (DE-588)4113782-6 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4113782-6 |
| title | A brief introduction to spectral graph theory |
| title_auth | A brief introduction to spectral graph theory |
| title_exact_search | A brief introduction to spectral graph theory |
| title_full | A brief introduction to spectral graph theory Bogdan Nica |
| title_fullStr | A brief introduction to spectral graph theory Bogdan Nica |
| title_full_unstemmed | A brief introduction to spectral graph theory Bogdan Nica |
| title_short | A brief introduction to spectral graph theory |
| title_sort | a brief introduction to spectral graph theory |
| topic | Kombinatorik (DE-588)4031824-2 gnd Graphentheorie (DE-588)4113782-6 gnd |
| topic_facet | Kombinatorik Graphentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030516192&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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